A vector a of magnitude 8 units has two components. One is perpendicular to a and is of magnitude
6 units. What is the magnitude of the other component?
[Hint: They are ‘components’ not ‘rectangular component’]
Answers
Explanation:
Given A vector a of magnitude 8 units has two components. One is perpendicular to a and is of magnitude 6 units. What is the magnitude of the other component?
- Let the vector be represented by vector PQ and the component by PR.
- Therefore second component will be RQ
- So vectors PQ = PR + RQ
- Also QR^2 = PQ^2 + PR^2
- = 8^2 + 6^2
- = 64 + 36
- = 100
- Or QR = 10
Therefore magnitude of the other component is 10 units
Reference link will be
https://brainly.in/question/10130920
Magnitude of other component = 10 unit
Explanation:
Let say Vector a is on x axis
then Vector a = 8 i
One component is perpendicular to a and is of magnitude 6 units.
= 6 j
Let say other component be of magnitude b at angle α to x axis
=> bcosα i + bsinαj
bcosα i + bsinαj + 6 j = 8i
=> bcosα i + bsinαj = 8i - 6j
=> bcosα = 8
bsinα = - 6
Squaring both & adding then
b²cos²α + b²sin²α = 8² + (-6)²
=> b²(cos²α + sin²α ) = 64 + 36
=> b² = 100
=> b = 10
Magnitude of other component = 10 units
Learn more:
The magnitude of x component of the position vector of a particle is 3 ...
https://brainly.in/question/11911867
the resultant of two vectors is perpendicular to one of them and has ...
https://brainly.in/question/11148654
if the magnitude of the resultant of two vectors of the same ...
https://brainly.in/question/12207216